The number of House Republicans who are unhappy with the party's strategy that has resulted in a government shutdown is small, but it is growing and nearing the point that would give Democrats enough votes to pass a bill - if the GOP allowed a vote.

So far, 14 Republican members of the House have publicly stated their willingness to vote for a clean CR - a continuing resolution to fund the government without any conditions attached.

The bills offered by the Republicans so far insist on defunding Obamacare or delaying parts of it.

If every House Democrat were to vote for a clean CR, then only 17 Republican votes would be needed for such a measure to pass.

But that would still require Republican leaders, who control the House, to allow such a measure to come for a vote.

Rep. Peter King, R-N.Y., reiterated this to a group of reporters on Tuesday when he said: "All I know is I think this shutdown's a bad idea and I want a clean CR."

Rep. Devin Nunes., R-Calif., echoed King's sentiment saying, "If you're going to take these extreme measures, you better have a plan to win, and I don't know if there's a plan to win."

At least six of the Republicans come from districts that voted for President Obama in 2012 and four others come from districts that voted for Obama in 2008 but flipped to Romney in 2012.

According to an ABC News count, these 14 Republicans would be willing to vote for a budget that does not include any changes to Obamacare:

Lou Barletta (Pa.)

Charlie Dent (Pa.)

Mike Fitzpatrick (Pa.)

Randy Forbes (Va.)

Michael Grimm (N.Y.)

Peter King (N.Y.)

Frank LoBiondo (N.J.)

Pat Meehan (Pa.)

Devin Nunes (Calif.)

Erik Paulsen (Minn.)

Scott Rigell (Va.)

Jon Runyan (N.J.)

Rob Wittman (Va.)

Frank Wolf (Va.)